# point of inflection for discontinuous function

I have a doubt on graph of $f(x) = \frac{x-5}{x+6}$. Is there a point of inflection on $x=-6$? The graph changes it nature from concave up to concave down but $f''(x)$ is not equal to zero anywhere.

• $x = -6$ is not in the domain of $f$ so it cannot be considered as a point of inflection. – DeepSea Dec 5 '16 at 6:38
• Yeah that's true. But as per the definition of point of inflection the concativity changes so isn't that be a point of inflection? will there be any other point of inflection for this graph? – Rohit Gulabwani Dec 5 '16 at 6:41
• there is none ! – DeepSea Dec 5 '16 at 6:42
• Concavity is opposite on disjoint intervals. There is no inflection point, nor is one required to exist. – dxiv Dec 5 '16 at 6:46
• If a graph is defined for x>=0 so can x=0 have a relative maxima or minima? – Rohit Gulabwani Dec 5 '16 at 6:53